Area of a Square

Area of a Square

Using the definition of area, we can calculate the sum of unit squares for any object with a closed space. In the case of a square, a square has a defined length and width.

In the simulation below, you can input an arbitrary length and width of your choice. Note that there are small unit squares on the graph, which can be counted manually to get the area of the square. Although we would get the correct answer, this is not practical as a rectangle with a large enough length and width would take a long time to count up all the individual unit squares each of length and width 1m by 1m.

Side:

An equation we can create therefore to calculate the area of a square is length times width.

\[ A = l \times w \]

Since we are dealing with a square however, this means that both the length and width of the square must be equal to each other. We can therefore simplify this equation by saying that the area is the lengths, or sides of the square squared.

\[ A = s \cdot s \]

or

\[ A = s^2 \]

Since a square is an enclosed space on the xy plane, that would mean that the units would be meters squared: \[ m^2 \]

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